Deep semantic interpretation of natural language is notoriously difficult. Despite extensive research on meaning representation spanning several decades, there still is no universally accepted method of representing sentence meanings, much less constructing them from text. Only partial solutions exist for disambiguating natural language expressions and for reference resolution.
One of the problem areas is the interpretation of syntactic ambiguities, such as the attachment of prepositional phrases.
Improvements in deep semantic interpretation could enable breakthroughs in, e.g., machine translation, search, information extraction, spam filtering, computerized assistance applications, computer-aided education, and many other applications intelligently processing information expressed in natural language, including the natural language control of robots and various home and business appliances.
State of the art in word sense disambiguation has been recently surveyed in R. Navigli: Word Sense Disambiguation: A Survey, Computing Surveys, 41(2), pp. 10:1-10:69, February 2009.
An introduction and survey of the problem of disambiguating prepositional attachments can be found in T. Baldwin et al: Prepositions in Applications: A Survey and Introduction to the Special Issue, Computational Linguistics, 35(2):119-149, June 2009.